检查是否可以通过加倍或三倍使数组相等
给定一个包含 n 个元素的数组。您可以将数组中的元素加倍或加倍。在所有操作之后检查是否可以使数组中的所有元素相等。
例子 ：
Input : A[] = {75, 150, 75, 50}
Output : Yes
Explanation : Here, 75 should be doubled twice and
150 should be doubled once and 50 should be doubled
once and tripled once.Then, all the elements will
be equal to 300.
Input : A[] = {100, 151, 200}
Output : No
Explanation : No matter what we do all elements in
the array could not be equal.
这个想法是重复将每个元素除以 2 和 3，直到元素可整除。在这一步之后，如果所有元素都相同，那么答案是肯定的。
这是如何运作的？我们知道每个整数都可以表示为素数2 a .3 b .5 c .7 d ..... 的乘积。因此，在我们的问题中，我们可以通过加倍（*2）或三倍（*3）来增加 a 和 b。我们可以通过乘以 2 或 3 使数组中所有元素的 a 和 b 相等。但是这些数字在它们的乘积表示中也有其他素数，我们不能改变它们的幂。因此，要使所有数字相等，它们应该从一开始就对其他素数具有相等的权力。我们可以通过将所有数字尽可能多地除以二或三来检查它。那么他们都应该是平等的。
C++
// C++ program to check if all numbers can
// be made equal by repeated division of 2
// and 3
#include
using namespace std;
bool canMakeEqual(int a[], int n)
{
for (int i = 0; i < n; i++) {
// continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
int main()
{
int A[] = { 75, 150, 75, 50 };
int n = sizeof(A) / sizeof(A[0]);
if (canMakeEqual(A, n))
cout << "Yes";
else
cout << "No";
return 0;
} Java
// Java program to check if all numbers can
// be made equal by repeated division of 2
// and 3
import java.util.*;
class GFG {
static Boolean canMakeEqual(int a[], int n)
{
for (int i = 0; i < n; i++) {
// Continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// Continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
public static void main(String[] args)
{
int A[] = { 75, 150, 75, 50 };
int n = A.length;
if (canMakeEqual(A, n))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by 'Gitanjali'.Python3
# Python3 code to check if all numbers can
# be made equal by repeated division of 2
# and 3
def canMakeEqual( a , n ):
for i in range(n):
# continuously divide every number by 2
while a[i] % 2 == 0:
a[i] = int(a[i] / 2)
# continuously divide every number by 3
while a[i] % 3 == 0:
a[i] = int(a[i] / 3)
# Check if all numbers same
for i in range(1,n):
if a[i] != a[0]:
return False
return True
# Driver Code
A = [ 75, 150, 75, 50 ]
n = len(A)
print("Yes" if canMakeEqual(A, n) else "No")
# This code is contributed by "Sharad_Bhardwaj".C#
// C# program to check if all numbers can
// be made equal by repeated division of 2
// and 3
using System;
class GFG {
static Boolean canMakeEqual(int []a, int n)
{
for (int i = 0; i < n; i++) {
// Continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// Continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
public static void Main()
{
int []A = { 75, 150, 75, 50 };
int n = A.Length;
if (canMakeEqual(A, n))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code is contributed by 'vt_m'.PHP
Javascript
输出 ：
Yes